Realizations in Biostatistics

Thursday, March 19, 2015

Full disclosure here: at one time I wanted to be a complementary and alternative (CAM) researcher. Or integrative, or whatever the cool kids call it these days. I thought that CAM research would yield positive fruit if they could just tighten up their methodology and leave nothing to question. While this is not intended to be a discussion of my career path, I’m glad I did not go down that road.

This article is a discussion of why. The basic premise of the article is that positive clinical trials do not really provide strong evidence of an implausible therapy, for much the same reason that doctors will give a stronger test to an individual who tests positive for HIV. A positive test will provide some, but not conclusive, evidence for HIV simply because HIV is so rare in the population. The predictive value of even a pretty good test is poor. And the predictive value of a pretty good clinical trial is pretty poor if the treatment has not been established.

Put it this way, if we have a treatment that has zero probability of working (the “null hypothesis” in statistical parlance), there will be a 5% probability that it will show a significant result in a conventional clinical trial. But let’s turn that on its head using Bayes Rule:

That is to say, if we know the treatment is useless, the clinical trial is going to offer no new knowledge of the result, even if it was well conducted.

Drugs that enter in human trials are required to have some evidence for efficacy and safety, such as that gained from in vitro and animal testing. The drug development paradigm isn’t perfect in this regard, but the principle of the requirement of scientific and empirical evidence for safety and efficacy is sound. When we get better models for predicting safety and efficacy we will all be a lot happier. The point is to reduce the probability of futility to something low and maximize the probability of a positive trial given the treatment is not useless, which would result in something like:

Of course, there are healthy debates regarding the utility of the p-value. I question it as well, given that it requires a reference to trials that can never be run. These debates need to be had among regulators, academia, and industry to determine the best indicators of evidence of efficacy and safety.

But CAM studies have a long way to go before they can even think about such issues.

Monday, March 16, 2015

Sometimes Facebook’s suggestions of things to read lead to some seriously funny material. After clicking on a link about vaccines, Facebook recommended I read an article about health outcomes in unvaccinated children. Reading this rubbish made me as annoyed as a certain box of blinking lights, but it again affords me the opportunity to describe how people can confuse, bamboozle, and twist logic using bad statistics.

First of all, Health Impact News has all the markings of a crank site. For instance, its banner claims it is a site for “News that impacts your health that other media sources may censor.” This in itself ought to be a red flag, just like Kevin Trudeau’s Natural Cures They Don’t Want You to Know About.

But enough about that. Let’s see how this article and the referred study abuses statistics.

First of all, this is a bit of a greased pig. Their link leads to a malformed PDF file on a site called vaccineinjury.info. The site’s apparent reason for existence is to host a questionnaire for parents who did not vaccinate their children. So I’ll have to go on what the article says. There appeNo study of health outcomes of vaccinated people versus unvaccinated has ever been conducted in the U.S. by CDC or any other agency in the 50 years or more of an accelerating schedule of vaccinations (now over 50 doses of 14 vaccines given before kindergarten, 26 doses in the first year).ars to be another discussion on the vaccineinjury.info site, which I’ll get to in a moment.

The authors claim

No study of health outcomes of vaccinated people versus unvaccinated has ever been conducted in the U.S. by CDC or any other agency in the 50 years or more of an accelerating schedule of vaccinations (now over 50 doses of 14 vaccines given before kindergarten, 26 doses in the first year).

Here’s one. A simple Pubmed search will bring up others fairly quickly. These don’t take long to find. What happens after this statement is a long chain of unsupported assertions about what data the CDC has and has not collected, that I really don’t have an interest in debunking right now (and so leave as an exercise).

So on to the good stuff. They have a pretty blue and red bar graph that’s just itching to be shredded, so let’s do it. This blue and red bar graph is designed to demonstrate that vaccinated children are more likely to develop certain medical conditions, such as asthma and seizures, than unvaccinated children. Pretty scary stuff, if their evidence were actually true.

One of the most important principles in statistics is defining your population. If you fail at that, you might as well quit, get your money back from SAS, and call it a day, because nothing that comes after that is meaningful. You might as well make up a bunch of random numbers if that’s the case, because that will be just as meaningful.

This study fails miserably at defining its population. The best I can tell, the comparison is between a population in an observation study called KIGGS and respondents to an open invitation survey conducted at vaccineinjury.info.

What could go wrong? Rhetorical question.

We don’t know who responded to the vaccineinjury.info questionnaire, but it is aimed at parents who did not vaccinate their children. This pretty much tanks the rest of their argument. From what I can tell, these respondents seem to be motivated to give answers favorable to the antivaccine movement. That the data they present are supplemented with testimonials gives this away. They are comparing apples to rotten oranges.

The right way to answer a question like this is a matched case-control study of vaccinated and unvaccinated children. An immunologist is probably the best one to determine which factors need to be included in the matching. That way, an analysis conditioned on the matching can clearly point to the effect of the vaccinations rather than leave open the questions of whether the differences in cases were due to differences in inherent risk factors.

I’m wondering if there isn’t some ascertainment bias going on as well. Though I really couldn’t tell what the KIGGS population was, it was represented as the vaccinated population. So in addition to imbalances in risk factors, I’m wondering if the “diagnosis” in the unvaccinated population was derived from the parents were asked which medical conditions their children have. In that case, we have no clue what the real rate is like, because we are comparing parents’ judgments (and parents probably more likely to ignore mainstream medicine at that) with, presumably, a GP’s more rigorous diagnosis. That’s not to say that no children in the survey were diagnosed by an MD, but without that documentation (which this web-based survey isn’t going to be able to provide), the red bars in the pretty graph are essentially meaningless. (Which they were even before this discussion.)

But let’s move on.

The vaccineinjury.info cites some other studies that seem to agree with their little survey. For instance, McKeever, et al. published a study in the American Journal of Public Health in 2004 from which the vaccineinjury.info site claims an association between vaccines and the development of allergies. However, that apparent association, as stated in the study, is possibly the result of ascertainment bias (the association was only strong in a stratum with the least frequent GP visits). Even objections to the discussion of ascertainment bias leave the evidence of association of vaccines and allergic diseases unclear.

The vaccineinjury.info site also cites the Guinea-Bisseau study reported by Kristensen et al.in BMJ in 2000. They claim, falsely, that the study showed a higher mortality in vaccinated children.

They also cite a New Zealand study.

What they don’t do is describe how they chose the studies to be displayed on the web site. What were the search terms? Were these studies cherry-picked to demonstrate their point? (Probably, but they didn’t do a good job.)

What follows the discussion of other studies is an utter waste of internet space. They report the results of their “survey,” I think. Or somebody else’s survey. I really couldn’t figure out what was meant by “Questionnaire for my unvaccinated child ("Salzburger Elternstudie")”. The age breakdown for the “children” is interesting, for 2 out of the 1004 “children” were over 60! At any rate, if you are going to be talking about diseases in children, you need to present it by age, because, well, age is a risk factor in disease development. But they did not do this.

What is interesting about the survey, though, is the reasons the parents did not vaccinate their children, if only to give a preliminary notion of the range of responses.

In short, vaccineinjury.info, and the reporting site Health Impact News, present statistics that are designed to scare rather than inform. Proper epidemiological studies, contrary to the sites’ claims, have been conducted and provide no clear evidence to the notion that vaccinations cause allergies except in rare cases. In trying to compile evidence for their claims, they failed to provide evidence that they did a proper systematic review, and even misquoted the conclusions of the studies they presented.

Wednesday, December 31, 2014

By now, most of us know about Facebook’s algorithmic retrospectives, and, of course, how some people thought it could be cruel. Indeed, posts about some sorts of issues, such as divorces or deaths, can get a lot of “likes” (where the “like” button means something other than “like”) and comments, and therefore get flagged by whatever algorithm the Facebook data scientists came up with as a post worthy of a retrospective.

There are a lot of issues here. When someone “likes” a post, they do not necessarily mean they “like” the event the post is about. It could mean a number of different things, such as “I hear you,” or “I’m empathizing with you,” or even “Hang in there.” However, the algorithms treat all likes equal.

Comments, of course, carry much more sophisticated meaning, but are much harder to analyze especially in the presence of sarcasm. And algorithms that do analyze comments (or any free text) for sentiment will require a large training set of hand-coded comments. (Which I suppose Facebook does have the resources to generate.)

Which leaves a few ways of handling this problem:

Do nothing different. Which is probably my favorite solution, because I’d like to look back on the good, the bad, and the ugly. It’s my life, and I want to remember it. Besides, the event that really sucked at the time (say, a torn ACL leading to surgery) may lead to good things.

Add a “I don’t want to see this” button. Which was already accomplished by including an “X” button, but maybe not so obvious.

Eliminate the retrospective, which I don’t think anybody agrees is a good solution.

I suppose one day Facebook’s algorithm will be smart enough to withhold posts it knows people don’t want to review, but then that will open up another can of worms.

Tuesday, December 9, 2014

In my Facebook feed, a friend posted a very scary-looking study that links genetically engineered (GE) crops to the rise in 22 diseases. These are pretty fearsome diseases, too, like bile duct cancer and pelvis cancer. For instance1:

Second, I could just say "correlation is not causation." QED. Article debunked, and can be swept to the dustbin.

Third, I can point out the correlation between sales of organic produce and autism. (Yikes!) In fact, using the methods of this article, I can probably prove a significant correlation between sales of organic produce and bile cancer, kidney cancer, autism, or lipoprotein disorder deaths. We can all grab our glyphosate-coated pitchforks and demand reform!

However, I think there are some statistical lessons here, and it's sometimes good to deconstruct some misused and abused statistics. And trust me, the statistics in this article are seriously misused. In fact, it might be an interesting project for an introductory graduate statistics class to collect articles like this and critique them. I'll do it for fun here. There are others that can speak to the scientific aspects of the article, like how it disagrees with the results of a review of over a trillion meals fed that incorporate GE products. There's also other quibbles with the article, like how it sometimes conflates pesticide discussions with glyphosate (an herbicide), that others can deconstruct.

When deciding on how to summarize and analyze data statistically, it is essential to work with the nature of the data. This article fails on several counts. First, it smashes together data from two complete different sources without considering how the data are related. Now, I'm generally excited to see data from disparate sources linked and analyzed together, but it has to be done carefully. This is how they obtained their data on GE use:

From 1990-2002, glyphosate data were available for all three crops, but beginning in 2003 data were not collected for all three crops in any given year. Data on the application rates were interpolated for the missing years by plotting and calculating a best fit curve. Results for the application rates for soy and corn are shown in Figures 2 and 3. Because the PAT was relatively small prior to about 1995, the sampling errors are much larger for pre-1995 data, more so for corn than for soy. Also, data were not missing until 2003 for soy and 2004 for corn. For these reasons, the interpolated curves begin in 1996 for soy and 1997 for corn in Figures 2 and 3.

This is how they obtained epidemiological data:

Databases were searched for epidemiological data on diseases that might have a correlation to glyphosate use and/or GE crop growth based on information given in the introduction. The primary source for these data was the Centers for Disease Control and Prevention (CDC). These data were plotted against the amount of glyphosate applied to corn and soy from Figure 6 and the total %GE corn and soy crops planted from Figure 1. The percentage of GE corn and soy planted is given by: (total estimated number of acres of GE soy + total estimated number of acres of GE corn)/(total Estimated acres of soy + total estimated acres of corn)x100, where the estimated numbers were obtained from the USDA as outlined above.

This seems innocent enough, but there's already a lot of wrong happening here. It's good that they explained some of their data cleaning, though we can always stand for more transparency behind this step. It's not scientifically glorious to describe how you handle missing or sparse data, but mishandling such can certainly sink your Nobel prize work. It's also good to explain derived variables, though I haven't gone back and checked their math.

The first fatal error is how they link the data. They simply merge it by year. It's the obvious-seeming step that already tanks their analysis. This is the same kind of merging that links, say, sales of organic crops to autism. Mashing up data needs to be done in a scientifically valid way, and simply merging disparate data by year isn't going to cut it here. All these data they gathered are crude summaries, and they just strung them together by year without giving any thought to whether the subjects in the epidemiological database have any connection to the subjects in the GE database. Sloppy, and that right there can be enough to tank any analysis, even if the analysis were well done. Which this one wasn't.

The second fatal error is how they present the data. Take the Figure 16 above. This graph breaks so many rules of data presentation that Edward Tufte's head would probably explode just from looking at it. But let's dig a little deeper. The authors say they plotted incidence of disease (in Figure 16 it's age-adjusted deaths due to lipoprotein disorder) against GE and glyphosate use. However, if you want to get technical about it, they plot all three of these versus time. This is a very important distinction. If they plotted incidence versus GE use, then they would put GE use on the x-axis. However, they show incidence in bar graphs by time, GE use in a line graph by time, and glyphosate use by time. I'll explain why this is important in the discussion of the third fatal flaw. But let's move ahead with the graph. From what I've been able to figure out, the left y-axis goes with the bar graph and is in deaths per hundred thousand. The axis on the right does double duty and covers both % of GE planted and 1000 tons of glyphosate used. It took me a while to figure that out, and it's very sloppy design anyway (the two scales have nothing to do with each other). If you ever see a line plot with a left and right y-axis, get skeptical. Here, the left axis starts at 0 and ends at 2.75 or so, and the right axis starts at -20 (!) and ends at 85 or so. I can see why they chose the y-axis, but the right axis is very curious. The -20 is a terrible choice for the start of the right axis. It's an invalid value of % of GE crops planted and 1000s of tons of glyphosate used. “Yes, Monsanto, I used -20,000 tons of glyphosate. You owe me $50,000.” It seems that the origin and scale of the right y-axis was chosen specifically to make GE and glyphosate use appear to track closely with deaths. I usually choose incompetence over malice to explain motivations, but it's very challenging to support incompetence in this case. It takes talent and/or effort to choose axes like this. I'll leave a deconstruction of the other graphs as an exercise, perhaps for your graduate-level stats class.

The third and final fatal error is how they analyze the data. Their analysis is the statistical equivalent to bringing a knife to a gunfight. They basically take all the GE and epidemiological data, ignore the time component, and send it through your Stat 101 Pearson correlation estimator formula. They construct some p-values, unsurprisingly find a massively small p-value, declare victory, and hit the publish button. Problem is, they compute the wrong statistical summary using the wrong formula and use it to make the wrong inference. The Pearson correlation estimator they use is designed for independent data, not time series data (and they know it's time series data because they say so on p. 11). Time series data has a complex correlation structure, and thus estimating second-order parameters like correlations is a bit of a challenge. For instance, GE use this year is going to be heavily correlated to GE use last year, as are deaths from lipoprotein disorders. Does the correlation reflect a relationship between death and GE use, or death this year and death last year? The naïve estimate assumes the correlation is between death and GE use, and accounts nothing of the relationship between deaths this year and last year (in the stat world we call this autocorrelation). Though I haven't done the math, my guess is that the correlation between death and GE use will be greatly reduced if not disappear altogether if time is taken into account. And even if there is a nonzero, significant correlation, the fact of the matter is that there needs to be a stronger link than time between the GE data and epidemiological data.

As a bonus, the paper claims to find a link between GE crop use, glyphosate use, and a whole bunch of nasty stuff, but they never try to tease out whether the nasty stuff is attributable to glyphosate or GE crops.

In conclusion, the paper claims to find a strong link between GE crop use and glyphosate use, and a host of diseases. Given that their paper was so deeply methodologically flawed, they are unable to support their conclusions. This paper should not be considered as evidence of the dangers of GE crop use or glyphosphate use, but should rather be used as a showcase of "How Not to Do It."

Edit: I need to learn how to spell glyphosate.

Footnotes:1Swanson, Leu, Abrahamson, and Wallet. "Genetically engineered crops, glyphosphate and the deterioration of health in the United States." Journal of Organic Systems. 9(2), 2014. Figure 16.

Wednesday, August 7, 2013

Every year, the first week of August, we statisticians meet to get our statistics, networking, dancing, and beer on. With thousands in attendance, it's exhausting. I wonder about the quality of statistical work the second week of August.

Each conference seems to have a life of its own, so I tend to reflect on each one. Here's my reflection on this year's:

First, being in Montreal, most of us couldn't use smartphones. Thankfully, Revolution Analytics sponsored free WiFi. They also do great work with R. So we were all for the most part able to tweet.

The quality of talks was pretty good this year, and I've learned a lot. We even had one person describe simulations with a flowchart rather than indecipherable equations, and I strongly encourage that practice.

As a member of the biopharmaceutical section, I was struck by how few people take advantage of our awards. Of course, everybody giving a contributed or topic contributed talks is automatically entered into the best contributed paper competition. But we have a poster competition and student paper competition that have to be explicitly entered, and participation is low. This is a great opportunity.

The highlight of the conference, of course, was Nate Silver's talk, and he delivered admirably. The perhaps thousand statisticians in attendance needed the message: learn to communicate with journalists and teach them numbers need context. I also like his response to the question "statistician or data scientist?" Which was, of course, "I don't care what you call yourself, just do good work."

Monday, July 15, 2013

Larry Wasserman calls the use of noninformative priors a “lost cause.” I agree for the reasons he stated, and the fact that there are always better alternatives anyway. At the very least, there are the heavy-tailed “weakly informative priors” that put nearly all weight on something reasonable, such as small to moderate values of a variance, and little weight on stupid prior values, such as mean values on the order of 10100.

However, they’ll be around for years to come. Noninformative priors are nice security blankets, and we get to think that we are approaching a problem with an open mind. I guess open minds can have stupid properties as well.

I hope, though, that we will start thinking more deeply about the consequences of our assumptions especially about noninformative priors rather than feeling nice about them.

Sunday, April 28, 2013

One of the things I'm realizing from Massively Open Online Courses (MOOCs) -- those online free classes from universities that have seem to sprung up from almost nowhere in the last year and a half -- is that they offer a perfect opportunity to explore outside my field. At first (and this was even before the term MOOC was coined), I took classes there were just outside my field. For instance, I've been in clinical and postmarketing pharmaceutical statistics for over 10 years, and my first two classes were in databases and machine learning. I did this because I was aching to learn something new, but I figured that with a class in databases I could make our database guys in IT sweat a bit just by dropping some terms and showing some understanding of the basics. It worked. In addition, I wanted to understand what this machine learning field was all about, and how it was different from statistics. I accomplished that goal, too.

Since then, I have taken courses in the area of artificial intelligence/machine learning, sociology and networks, scientific computing (separately from statistical computing), and even entrepreneurship. I have also encouraged others to take part in MOOCs, though I don't know the result of that. Finally, I have come back to some classes I've already taken as a community TA, or former student who actively takes part in discussions to help new students take the class.

This is all valuable experience, and I could write several blog entries on the benefits. The main one I'm feeling right now is the feeling that I'm coming up for air, and taking a sampling of other points of view in a low-risk way. For example, though I don't actively use Fourier analysis in my own work, one recent class and one current class both use it to do different things (solve differential equations and process signals). Because these classes involve programming assignments, I've now deepened my understanding of the spectral theorem, which I only studied from a theoretical point of view in graduate school. I'm also thinking about this work from the point of view of time series analysis, which is helping me think about some problems involving longitudinal data at work.

From a completely different standpoint, another class helped me think about salary negotiations in terms of expected payoff (i.e. combination of probability of an offer being accepted vs. salary). This sort of analysis invited further analysis of the value of that job vs. what I would be paid and the insecurity of moving to a different job. In the end, I turned down what would have been a pretty good offer, because I decided it did not compensate for the risks I was incurring. The cool thing is that these were all applying concepts I already understood (expected value, expected payoff), but applied in a different way from what I was already doing.

The best thing about MOOCs is that the risk is low. All that is required is an internet connection and a decent computer. Some math courses may require a better computer to do high-powered math, but I've seen few that require expensive textbooks or expensive software. Even Mathworks is now offering Matlab at student pricing to people who are taking some classes, and Octave remains a free option for people unable to take advantage of it. And, if you are unable to keep up the work, there is now downside. You can simply unenroll.

Saturday, March 30, 2013

Tired of slides, I’ve been experimenting with different ways of presenting. At the recent Conference on Statistical Practice, I decided only to use slides for an outline and references. As it turns out, the most critical feedback I got had to do with the fact that the audience couldn’t follow the organization because I had no slides.

I tried presenting without slides because, well, I started to use them as a crutch. I also saw a lot of people presenting essentially by putting together slides and reading from them. So I figured I would expand my horizons.

Next time I present, I’ll do slides, I guess, but I may try something a bit different.

Wednesday, March 27, 2013

Caltech's Machine Learning MOOC is coming to an end this spring, with the final session starting on April 2. There will be no future sessions. The course has attracted more than 200,000 participants since its launch last year, and has gained wide acclaim. This is the last chance for anyone who wishes to take the course (http://work.caltech.edu/telecourse).Best.The Caltech Team

I strongly recommend this course if you can take it, even if you have taken other machine learning classes. It lays a great theoretical foundation for machine learning, sets it off nicely from classical statistics, and gives you some experience working with data as well.

If you were for some reason waiting for the right time, it looks to be now or never.